a) Correlation ρ = 1.0 δ3 = (0.6)^2(10)^2+(0.4)^2(20)^2+2(0.6*0.4*1*10*20) = 196
Variance of Portfolio = 196
b) Correlation ρ = 0.5 δ3 = (0.6)^2(10)^2+(0.4)^2(20)^2+2(0.6*0.4*0.5*10*20) = 148
Variance of Portfolio = 148
c) Correlation ρ = 0 δ3 = (0.6)^2(10)^2+(0.4)^2(20)^2+2(0.6*0.4*0*10*20) = 100
Variance of Portfolio = 100
19)
β=-0.25
a) As the beta is negative, the rate of return on the stock will go down when the market return goes up.
If market rises by an extra 5%, the stock goes down by -0.25*5= -1.25%. Stock return will be down by -1.25%.
If market falls by an extra 5%, the stock goes up by 0.25*5 = 1.25%. Stock return will be up by 1.25%.

b) Invested $1M in well-diversified portfolio.
We are looking to invest in the safest overall portfolio return i.e., the option that reduces our risk to the lowest value. Reducing risk is nothing but reducing beta. Investing in stocks with beta= 1 (option 2) is not a wise option because the overall portfolio return is equally impacted by the rate of market return. Investment in Treasury bills with beta =0 (option 1) is though not bad as option 2, it removes any sort of impact of the market return. However, there is neither gain nor loss due to market changes. Option 2 is only an option if someone is not willing to take any risk .i.e.., only looking for the risk free return. Option 3 with beta -02.5 is the best option as the stock return moves in opposite direction to the market and even a slightest drop of 0.25% market return can produce 0.25% increase of overall portfolio return. And with increase of 0.25% market return, the overall portfolio return will drop only by 0.25%. Therefore, the risk is lowered by option 3 and that is the best option of the three.

c) Margin of 50 %, twice the money of investor’s portfolio. Therefore, the risk in this case is twice that of the original risk. From question a, we derived S.D. of original portfolio as 19.875%
Standard deviation of this portfolio = 2 * 19.875 % = 39.75 %
Standard deviation of the portfolio δp = 39.75 %

c) The standard deviation of the portfolio is based on the average securities portfolio covariance and standard market investment.
Therefore, for 100 stocks like Dell with β = 1.41, the portfolio…

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